I have a Keithley 194A which can do this. It takes up to 32k x 16 bit samples at up to 100kHz. It can then calculate various things: average, RMS, StdDev, integral, derivative, peak, and others. Your application may be limited by the 16 bit resolution and inherent noise.
I did not get that far going through the old Keithley meters because I recognized it as being the high speed model. It might be a good default option if I cannot find anything better since it has real bandwidth specifications. I wonder what its low frequency noise spectrum looks like.
Haven't used it in a few years. But I believe my hp 3456A/34401A have it.
I was surprised that the HP multimeters following the HP 3456A could not do it so I did not search back that far. The HP 3456A can calculate the variance so standard deviation is one square root away.
I did not find anything about the HP 34401A calculating the standard deviation in the manual, but see below.
On the 34401A standard deviation doesn't come standard, but it can be enabled with the following instructions:
DIAG:POKE 28,0,1191 MATH Menu -> MIN-MAX: adds Standard Deviation and Peak-to-Peak
Why did HP hide this? I did not find anything about it.
There might a few that do it from the front panel, but AFAIK the typical way was acquire samples as fast as possible via GPIB and do all the calculations later and elsewhere. As mentioned, the 34401A appears to have this function although I have not tried it. If you contemplate acquring one I can try it out for you first.
It may come down to transferring the data and doing the calculation on a computer if I have to do it that way. I am initially looking for something simpler.
What bandwidth, sample rate and aperture are we talking about here?
Sample rate can be largely ignored assuming that it is fast enough because it does not affect standard deviation except in how it limits the aperture (integration time).
Except for the Keithley 194A high speed multimeter discussed above, none of the specifications I have gone through give bandwidth for DC measurements. Excluding limits by the signal conditioning, bandwidth is limited by the integration time (aperture) which produces a nonlinear sinc frequency response roughly equivalent to 0.468/t. For a 1 power line cycle measurement at 60 Hz, that will be 28 Hz.
For a spot noise measurement, the 28 Hz bandwidth limit from a 1 PLC measurement can to be taken into account as sort of an extra pole in the filter response. If a faster sample rate with a shorter integration time was used, then the increase in bandwidth would make this step unnecessary.
So I want a sample rate of at least 1 PLC, but would not object to something which is faster.